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Positive definite functionals in Banach spaces

Published online by Cambridge University Press:  09 April 2009

G. G. Hamedani
Affiliation:
Arya-Mehr University of Technology, Tehran, Iran. Michigan State University, U.S.A.
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Abstract

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We establish a version of Bochner Theorem due to S. Boylan for Banch spaces with a basis.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Boylan, S. L. (1975), ‘Positive definite functionals, function-space transforms and abstract Wiener spaces’, Duke Math. J., 42, 549557.CrossRefGoogle Scholar
Day, M. M. (1962), Normed linear spaces, 2ndrev. ed. (Academic Press, New York: Springer-Verlag, Berlin). MR26#2847.Google Scholar
Gross, L. (1963), ‘Harmonic analysis on Hilbert space’. Mem. Amer. Math. Soc 46. MR28≠4304.Google Scholar
Hamedani, G. G. and Mandrekar, V. (1973), ‘Inversion formulae for the probability measures on Banach spaces’, Trans. Amer. Math. Soc., 180, 143169.Google Scholar
Kuelbs, J. (1970), ‘Gaussian measures on a Banach space’. J. Functional Analysis 5, 354367. MR41≠4639.Google Scholar
Kuelbs, J. and Mandrekar, V. (1972), ‘Harmonic anlaysis on F-spaces with a basis’, Trans. Amer. Math. Soc. 169, 113152.Google Scholar
Sazanov, V. (1958), ‘Remarks on characteristic functionals’. Teor. Verojatnost. i Primenen. 3, 201205Google Scholar
Theor. Probability Appl. 3 (1958). 188192. MR20#4882.CrossRefGoogle Scholar